Letter abstract
Nature Materials 4, 391 - 394 (2005)
Published online: 17 April 2005 | doi:10.1038/nmat1374
Subject Categories: Metals and alloys | Computation, modelling and theory
Evolutionary approach for determining first-principles hamiltonians
Gus L. W. Hart1, Volker Blum2,4, Michael J. Walorski3 & Alex Zunger2
Modern condensed-matter theory from first principles is highly successful when applied to materials of given structure-type or restricted unit-cell size. But this approach is limited where large cells or searches over millions of structure types become necessary. To treat these with first-principles accuracy, one 'coarse-grains' the many-particle Schrödinger equation into 'model hamiltonians'1, 2, 3 whose variables are configurational order parameters (atomic positions, spin and so on), connected by a few 'interaction parameters' obtained from a microscopic theory3, 4. But to construct a truly quantitative model hamiltonian, one must know just which types of interaction parameters to use, from possibly 106–108 alternative selections. Here we show how genetic algorithms5, mimicking biological evolution ('survival of the fittest'), can be used to distil reliable model hamiltonian parameters from a database of first-principles calculations. We demonstrate this for a classic dilemma6 in solid-state physics7, structural inorganic chemistry8 and metallurgy9: how to predict the stable crystal structure of a compound given only its composition. The selection of leading parameters based on a genetic algorithm is general and easily applied to construct any other type of complex model hamiltonian from direct quantum-mechanical results.
- Department of Physics and Astronomy, Northern Arizona University, Flagstaff, Arizona 86011-6010, USA
- National Renewable Energy Laboratory, Golden, Colorado 80401, USA
- Computer Science Department, Northern Arizona University, Flagstaff, Arizona 86011-5600, USA
- Present address: Fritz-Haber Institut der Max-Planck-Gesellschaft, Faradayweg 4–6, 14195 Berlin, Germany
Correspondence to: Gus L. W. Hart1 e-mail: gus.hart@nau.edu
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